Solve the problem.
-The product of two consecutive integers is 5 more than their sum. Find the integers.
A) 3, 4 or -2, -1
B) -2 and -1
C) 2, 3 or -2, -1
D) 3 and 4

Question

Quizplus · Accepted Answer

Let the consecutive integers be $n$ and $n+1$. The equation based on the given information is $n(n + 1) = n + (n + 1) + 5$. Simplifying gives a quadratic equation $n^2 + n = 2n + 6$, which simplifies to $n^2 - n - 6 = 0$. Factoring this gives $(n - 3)(n + 2) = 0$, leading to $n = 3$ or $n = -2$, thus the consecutive integers are either 3 and 4 or -2 and -1.

Solve the Problem. -The Product of Two Consecutive Integers Is 5 More Than